Problem: Simplify the expression. $(4y^{2}-3y)(-4y^{4}+2y^{3}-5y)$
Answer: First use the distributive property. $ 4 y^2 (-4 y^4) + 4 y^2 (2 y^3) + 4 y^2 (-5 y) - 3 y (-4 y^4) - 3 y (2 y^3) - 3 y (-5 y) $ Simplify. $ - 16y^{6} + 8y^{5} - 20y^{3} + 12y^{5} - 6y^{4} + 15y^{2} $ $-16y^{6}+20y^{5}-6y^{4}-20y^{3}+15y^{2}$ Identify like terms. $ {- 16y^{6}} {+ 8y^{5}} {- 20y^{3}} {+ 12y^{5}} {- 6y^{4}} {+ 15y^{2}} $ Add the coefficients. $ { -16y^{6}} {+ 20y^{5}} { -6y^{4}} { -20y^{3}} {+ 15y^{2}} $